How many ray tracing samples they used in theater animation?
Depends.

The thing that you noticed was that it looked good. That is the target, not a certain number of samples.

You may have noticed for instance that a glass shader typically needs more samples than a diffuse shader. Once you have determined a ratio of samples that looks good (assuming you are using branched path-tracing which separates out the number of samples each type of shader uses per pass), then you can turn up the samples to produce higher quality results.

If you are trying to reduce fireflies, that is a separate question that has already been answered here.

Computer specs don't really matter either, as it is more a matter of what gets the job done in a certain amount of time within budget. The more computers and/or more powerful computers you throw at the "problem" of rendering, the easier it becomes to quickly produce animation.